Adomian Decomposition Method Using Integrating Factor

This paper proposes a new Adomian decomposition method by using integrating factor.Nonlinear models are solved by this method to get more reliable and efficient numerical results.It can also solve ordinary differential equations where the traditional one fails.Besides,the complete error analysis for this method is presented.     

The Viscous Surface-Internal Wave Problem: Nonlinear Rayleigh–Taylor Instability

We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a rigid bottom in a three-dimensional horizontally periodic setting. The effect of surface tension is either taken into account at both free boundaries or neglected at both. We are concerned with the Rayleigh–Taylor instability, so we assume that the upper fluid is heavier than the lower fluid. When the surface tension at the free internal interface is below a critical value, which we identify, we establish that the problem under consideration is nonlinearly unstable.     

Optimization of Solution Condition for an Effective Electrochemical Reduction of N2O

An effective electrochemical reduction of nitrous oxide (N₂O) is established by controlling solution compositions in this study. N₂O was electrochemically reduced varying solvent composition and supporting electrolytes (K₂SO₄ and Na₂SO₄) concentrations. The differences in reduction current density and solution resistance were analyzed via linear sweep voltammetry (LSV) and electrochemical impedance spectroscopy (EIS), respectively, depending on solution conditions. UV‐Vis spectroscopy was adopted to measure the solubility of N₂O. As a result, among the conditions investigated in this study, 300 mM of K₂SO₄ and aqueous based solution were revealed as an optimum condition for the electrochemical N₂O reduction. At 300 mM of K₂SO₄, the highest current density was obtained due to a high conductance of the electrolyte and a moderate solubility of N₂O.     

传输线方程的高精度龙格−库塔数值求解方法

提出了一种求解传输线方程的高精度龙格-库塔(RK)方法。此方法在空间上采取高阶泰勒展开,提高了对空间微分的近似精度,减少了数值色散所带来的误差。与传统的时域有限差分法(FDTD)方法相比,在每波长采样数相同时,RK方法的计算精度更高。同时,根据Taylor模型,对外界平面波激励源进行离散,成功利用RK方法对外部场激励传输线进行求解,扩大了龙格-库塔方法在求解传输线方程时的应用范围。通过编程对平面波辐照下无限大地平面上的单导体与双导体的算例分别应用FDTD方法与RK方法进行了计算,验证了RK方法的正确性。结果表明同等计算条件下RK方法的计算精度更高。     

关于Taylor公式中Lagrange余项的再研究

在Azpeitja对Taylor公式中Lagrange余项的"中间点"渐近性的研究基础上,又建立几个易于验证和推广的结果.     

Laplacian growth without surface tension in filtration combustion: Analytical pole solution

Filtration combustion (FC) is described by Laplacian growth without surface tension. These equations have elegant analytical solutions that replace the complex integro‐differential motion equations by simple differential equations of pole motion in a complex plane. The main problem with such a solution is the existence of finite time singularities. To prevent such singularities, nonzero surface tension is usually used. However, nonzero surface tension does not exist in FC, and this destroys the analytical solutions. However, a more elegant approach exists for solving the problem. First, we can introduce a small amount of pole noise to the system. Second, for regularization of the problem, we throw out all new poles that can produce a finite time singularity. It can be strictly proved that the asymptotic solution for such a system is a single finger. Moreover, the qualitative consideration demonstrates that a finger with of the channel width is statistically stable. Therefore, all properties of such a solution are exactly the same as those of the solution with nonzero surface tension under numerical noise. The solution of the Saffman–Taylor problem without surface tension is similar to the solution for the equation of cellular flames in the case of the combustion of gas mixtures. © 2014 Wiley Periodicals, Inc. Complexity 21: 31–42, 2016     

Generating the patterns of variation with GeoGebra: the case of polynomial approximations

In this paper, we report a teaching experiment regarding the theory of polynomial approximations at the university mathematics teaching in Sweden. The experiment was designed by applying Variation theory and by using the free dynamic mathematics software GeoGebra. The aim of this study was to investigate if the technology-assisted teaching of Taylor polynomials compared with traditional way of work at the university level can support the teaching and learning of mathematical concepts and ideas. An engineering student group (n = 19) was taught Taylor polynomials with the assistance of GeoGebra while a control group (n = 18) was taught in a traditional way. The data were gathered by video recording of the lectures, by doing a post-test concerning Taylor polynomials in both groups and by giving one question regarding Taylor polynomials at the final exam for the course in Real Analysis in one variable. In the analysis of the lectures, we found Variation theory combined with GeoGebra to be a potentially powerful tool for revealing some critical aspects of Taylor Polynomials. Furthermore, the research results indicated that applying Variation theory, when planning the technology-assisted teaching, supported and enriched students’ learning opportunities in the study group compared with the control group.     

一种基于最优频段的X射线脉冲星累积轮廓时延估计方法

为提高X射线脉冲星导航中累积脉冲轮廓的时间延迟估计精度, 分析了X射线脉冲星累积脉冲轮廓的频谱特性和现有Taylor快速傅立叶变换时延估计算法的缺陷, 提出了一种基于最优频段的累积轮廓时延估计算法, 并通过建立不同信噪比下时延估计误差与所采用频段之间的关系以确定最优频段. 数值及实测数据实验结果表明: 在短时观测或光子流量较小时, 该算法优于常用的近似最大似然 (FAML)、相关 (CC)、最小二乘 (NLS) 及加权最小二乘 (WNLS) 方法; 在观测时间较长或光子流量较大时, 该算法的估计精度与CC及NLS方法相当, 但其运算量低于NLS, FAML 及WNLS方法. 本文所提算法适用于短时观测脉冲轮廓或低流量脉冲星的高精度时延估计.